Read the situations in the table below. Then drag a graph and equation to represent each situation. Indicate whether each of the relationships is proportional or non-proportional.
Answers
The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
What are linear equations?
Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, graph 1 varies 4 times the x value every time there is an increase of 1 in the x-axis and in graph 2 it is a linear equation with intercept at 4 and thus the graph increases with +4 and A proportional relationship exists between two values x and y when they can be expressed in the general form y = kx,
Hence, The equation for situation 1 is y=4x and is directly proportional and the situation two will have equation y=x+4 and is not proportional.
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Related Questions
What is the equation of a line with a slope of 3 and a point (3. 1) on the line? Express the equation in the form of y Enter your answer in the box mz+ b where m is the slope and b is the y-intercept
Answers
A line with a slope of three and the point three on the line have the equation y=3 z+1. The equation of a straight line can be found using the formula y = mx + b.
What do you meant by y-intercept ?If a line has a slope of 3 and a y intercept of 1, you need to determine its equation. Remember the line's equation by first going back: when y=mz+b , M is the slope, and Y-intercept b is the value.
In order to solve for y in the equation y=m z+b, all you need to do is swap out m for 3, the slope you provided, and b for 1, the y-intercept. The line's equation is given by y=3 z+1, where z represents the line's y-intercept and slope. If you are aware of the slope of the line being studied and the provided point is also the y intercept, you can utilise the slope intercept formula, y=mx+b (0,b).
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7. {MCC.7.G.2} *
Which set of numbers cannot
represent the lengths of the sides
of a triangle?
A) 7, 9, 12
B) 8, 6, 7
C) 8, 20, 12
D) 10, 13, 20
O A
B
O D
Answers
If
f
(
x
)
=
2
x
4
−
9999999kwwkqkkaosos
use partial quotients to solve
5,140÷9=
Answers
Answer: 571.11111...(Fraction: 9/28)
Step-by-step explanation:
5,140÷9 = 571.11111...
95 POINTS!!! To increase business, the owner of a shoe store is running a promotion in which a customer's bill can be selected at random to receive a discount. When a customer's bill is printed, a program in the cash register determines randomly whether the customer will receive a discount on the bill. The program was written to generate a discount with a probability of 0.15; that is, 15% of the bills get a discount in the long run. However, the owner is concerned the program is incorrect and is not generating the intended long-run proportion of 0.15.
The owner selects a random sample of bills and finds that only 12% of them received a discount. A confidence interval for p, the proportion of bills that will receive a discount in the long run, is 0.12 ± 0.05, and all conditions for inference are met.
Consider the confidence interval 0.12 ± 0.05.
Part A: Does the confidence interval provide convincing statistical evidence that the program is not working as intended? Justify your answer. (3 points)
Part B: Does the confidence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.15? Justify your answer. (2 points)
Part C: A second random sample of bills is taken that is six times the size of the original sample. In the second sample, 12% of the bills received the discount. Determine the value of the margin of error based on the second sample of bills used to compute an interval for p with the same confidence level as that of the original interval. (2 points)
Part D: Based on the margin of error in part C that was obtained from the second sample, is the program working as intended? Justify your answer.
Answers
An area surrounding a measurement that indicates how accurate it is called a confidence interval.
Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.
Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:
p ± Zα/2[√{P(1 –p)/n}] ……(1)
where
Zα/2 is the upper (α/2)% point of N(0, 1),
pcap = sample proportion, and
n = sample size.
One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)
Now to work out the solution,
The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)
for Part (a)
equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.
for Part (b)
equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.
For Part (c)
Margin of error is: Zα/2[√{P(1 –P)/n}]
If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be
[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]
= √(n1/n2)
= 1/√6 [given the second sample size is 6 times the first sample size]
= 0.4082
= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082
= 0.05 x 0.4082
= 0.020.
Thus, the margin of error when the sample size if 6-fold is 0.020.
For Part (d)
The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.
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Exit ticket for geometry
Answers
Answer:
y = 10
Step-by-step explanation:
given DEFG = SPQR
QR = FG
=> 2x - 4 = 12
=> 2x = 16
=> x = 8
angle PQR = EFG
=> 6y + x = 68
=> 6y + 8 = 68
=> 6y = 60
=> y = 10
8. Each day, Amy walks to school. She leaves her home
and walks south 7 blocks to her friend's house. They then
turn to the west and walk 12 blocks to the school. At the
end of the day, Amy walks directly from the school to
her home.
a) To the nearest tenth (one decimal place), how many
blocks does Amy walk on her way home?
<+
-10
-10
Home s
-5
Friend's house
-5
-10
5
10
School
S
b) How many blocks does Amy walk in one day for her round trip to the school and back
home? Round to the nearest tenth.
Answers
32. 9 blocks for b
Explanation below
Answer:
(a) 13.9 blocks (nearest tenth)
(b) 32.9 blocks (nearest tenth)
Step-by-step explanation:
The given scenario can be modeled as a right triangle.
If Amy walks south 7 blocks, one leg of the triangle is 7.
If Amy then walks west 12 blocks, the other leg of the triangle is 12.
Part (a)To calculate the number of blocks Amy walks on her way home if she walks directly from school to her home, find the length of the hypotenuse of the right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Substitute a = 7 and b = 12 into Pythagoras Theorem and solve for c (hypotenuse):
[tex]\implies 7^2+12^2=c^2[/tex]
[tex]\implies 49+144=c^2[/tex]
[tex]\implies 193=c^2[/tex]
[tex]\implies c=\sqrt{193}[/tex]
[tex]\implies c=13.8924439894...[/tex]
Therefore, Amy walks 13.9 blocks (nearest tenth) on her way home.
Part (b)To calculate the number of blocks Amy walks in one day for her round trip to school and back home, sum the side lengths of the right triangle:
[tex]\implies 7 + 12 + 13.9 = 32.9[/tex]
Therefore, Amy walks 32.9 blocks (nearest tenth) in one day for her round trip to school and back home.
graph f and h , write h in terms of f, describe the transformation from the graph of f to the graph of h .
the equation :
f(x) = 3x ; h(x) = 3x - 5
Answers
h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
What is the graph of the function?A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.
Here,
We can draw the graph as
h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)
h(x) = f(x) + 5
The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.
Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
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Ryan spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6300 feet.
Ryan initially measures an angle of elevation of 15 to the plane at point A. At some
later time, he measures an angle of elevation of 31 to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest foot if necessary.
Answers
If Ryan spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The distance the plane traveled from point A to point B is: 13,027ft .
How to find the distance?Constant altitude =6300 feet
Angle of elevation =15 to the plane at point A
An angle of elevation =31 to the plane at point B.
So,
Tan 15° = 6300/ON
ON =23,511.92
Tan 31° =6300/OB
OB = 10,484.96
So,
AB =23,511.92 - 10,484.06
AB = 13,026.96
AB = 13,027ft (Approximately)
Therefore the distance is 13,027ft.
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You are given 2 parallel lines on the coordinate plane. You are told to translate x + 3,y-2, rotate 180° clockwise about the origin, then reflect over the y-axis. After the transformations you will have what type of lines?
A Intersecting lines
B. The Same Line
C. Parallel Lines
Answers
Since matching angles are formed and the equal corners are congruent when a line joins two parallel lines, one of the choices isc=d.
Parallel lines are what?Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.
Here,
Given : vertical angles, A = d also represents a solution.
B+d=180 as a result of b+c=180 therefore
B+d=180 as a result of b+c=180 therefore Since a=d, c=d, and b+d=180, the answer is B,C,E.
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The graph shows money in dollars as a function of time
in days. Write an equation for the function, and
describe a situation that it could represent. Include the
initial value, rate of change, and what each quantity
represents in the situation.
Answers
Each quantity represents in the situation are y is overall financial time (day). 10 times the daily wage earned. 25 times the money's initial worth.
What each quantity represents in the situation.The graph shows money in dollars as a function of time ,an equation for the function, and describe a situation that it could represent. Include the
initial value, rate of change
The slope is equal to 10 10 (simplify) = 175-75 / 15-5 100
y - 75 = 10(x - 5) (x - 5)
4 - 75 = 10x - 50 y - 75 + 75 = 10x - 10 + 75 y = 10x + 2.5
If you start with $25 and can make $10 every day, money do you have after x days are
y = overall financial time (day).
10 times the daily wage earned.
25 times the money's initial worth.
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($75,000 - $80,000) x (1 - .21)
Answers
Answer:
-3,950
Step-by-step explanation:
First -5,000(1-0.21)
Then multiply -5,000 x 0.79 = -3,950
Please answer question 10 and 11 please
Answers
Answer:
d7-dx=(20x|x-3|+40)x x-3 (|x-3+2)x| x-3|
Step-by-step explanation:
Hope this helps :D
Given it was not a strike, what is the probability it was a knuckle
ball? Enter the answer as a percent (%)to the nearest tenth.
Answers
In response to the above problem, we may state that the triangle's - 5/13 measurements correspond to sin and cos.
Trigonometric functions: what are they?The first six essential trigonometric functions are used in trigonometry. These functions are trigonometric ratios. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six basic trigonometric functions. The side ratio of a right-angled triangle is equivalent to the identities and functions of trigonometry. Trigonometric formulas are applied to the perpendicular side, hypotenuse, and base of a right triangle in order to calculate the sine, cosine, tangent, secant, and cotangent values.
as base/hypotenuse = cos x
and sin x = hypotenuse/perpendicular
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pls help last test or semester half my grade pls pls pls i’ll give brainliest
Answers
Therefore , the solution of the given problem of function comes out to be satisfies the given function is x=9 and y=21.
What is function?Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.
Here,
Given : A table of values of x and y
To find : the function is linear or not
Thus,
F(x) = y -3x =0
So,
Putting the values of x and y in given function
The value which satisfies the given function is x=9 and y=21.
Therefore , the solution of the given problem of function comes out to be
satisfies the given function is x=9 and y=21.
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how to figure out how many data points are in a data set
Answers
Answer:
Step-by-step explanation:
read the data numbers
do two rectangle prisms have the same volume? Sometimes, always, never. Pls explain! Giving brainlyst :3
Answers
Answer:
It is a known fact that there are rectangular prisms with the same volume but different dimensions.
Karen and Kate have 50 CDs between them. Karen has 6 less than kate. How many each has?
Answers
Answer:
19
Step-by-step explanation:
Karen and Kate have 50 CDs between them. Karen has 6 less than kate. How many each has?
25&25
If Karen Has 6 Less Then Kate, Karen Would Have 19 CDS
Hope This Helps
•50 POINTS HELP• guessers will be reported.
If P=(4,7), Find: D2 (p)
Answers
The answer is distance from P to l. is equal to square root of 2
Find the distance from P to l ?Line I contains points (0, -3) and (7,4). Point P has coordinates (4,3)
Find the slope of line l we have the points (0, -3) and (7,4)
m=(4+3)/(7-0) m=7/7 m=1
Find the equation of the line perpendicular to the line l that passes through the point P
Remember that
If two lines are perpendicular, then the product of their slopes is equal to -1, the slope of the perpendicular line is
m=-1 .Find the equation in point slope form
y-y1=m(x-x1)
(x1,y1)=P(4,3)
substitute
y-3=-1(x-4)
y-3=-x+4
y=-x+7
m=1 (see the step 1)
and we have the point (0,-3) -----> y-intercept
so the equation of the line l is
y=x-3
Find the intersection point line l and its perpendicular line
y=x-3 ------> equation A
y=-x+7 -----> equation B
solve the system of equations
Adds equation A and equation B
2y=-3+7
2y=4
y=2
substitute in equation A
2=x-3 x=2+3 x=5
the intersection point is (5,2)
Find the distance between point (5,2) and point P(4,3)
Remember that, this distance is the distance from P to l.
the formula to calculate the distance between two points is equal to
we have
(x1,y1)=(5,2)
(x2,y2)=(4,3)
substitute in the formula
therefore
The answer is distance from P to l. is equal to square root of 2
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Given that a square root of a number N is a value, that when multiplied by itself, results in N. What's the square root of 49? a. 9, b. 5, c. 7, d. 8
Answers
Answer:
Step-by-step explanation:
[tex]N^{2} =49[/tex]
To solve take the square root of 49.
[tex]\sqrt{49}[/tex] = 7
Option c which is 7
Calculate the sample mean and sample variance for the following distribution of heights in centimeters for an 8 year old boy
Answers
Answer: To calculate the sample mean of a distribution, you add up all the values and divide by the number of values in the sample. The sample mean is also known as the average.
The formula for the sample mean is:
X-bar = (X1 + X2 + ... + Xn) / n
To calculate the sample variance of a distribution, you first need to calculate the sample mean. Then, for each value, you subtract the sample mean and square the result. You add up all these squared differences, and divide the sum by the number of values in the sample.
The formula for the sample variance is:
s^2 = ( (X1 - X-bar)^2 + (X2 - X-bar)^2 + ... + (Xn - X-bar)^2 ) / (n - 1)
It would be helpful to have the sample data, however I cannot complete this task without it.
Please provide me with the data.
Step-by-step explanation:
Which of the following is the correct equation for the trend line in the scatter plot?
Answers
The equation of the trend line will be : Y = (1/4)x - 1.
What is trend line in scatter plots?A trend line is a straight line that best represents the points on a scatterplot. The trend line may go through some points but need not go through them all.Given is a scatter plot a shown in the image.
The general equation of a straight line is -
y = mx + c
{m} - slope
{c} - intercept along the y - axis
We can find the slope as follows. The line passes through the points -
(4, 0) and (0, - 1). We can write -
m = (- 1 - 0)/(0 - 4)
m = - 1/-4
m = 1/4
and
[c] = - 1
So the equation of the trend line will be -
Y = (1/4)x - 1
Therefore, the equation of the trend line will be : Y = (1/4)x - 1.
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Please help with homework
Solve
2(x+4)=3(-2+x)
Answers
Answer:
x = 14
Step-by-step explanation:
2(x + 4) = 3( -2 + x) distribute the 2 and the 3.
2(x) + 2(4) = 3(-2) + 3(x)
2x + 8 = -6 + 3x Subtract 2x from both sides
2x - 2x + 8 = -6 +3x -2x
8 = -6 +x Add 6 to both sides
8 + 6 = 6 - 6 + x
14 = x
HELLPPPP ASAP PLEASE I NEED HELP WHOEVER GETS FIRST GETS BRAINLIEST AND 100 coinss
Answers
This is a simple cross multiplication problem! Any time you're given a ratio and then the actual quantity of something, you can use cross multiplication to figure out the quantity of the other thing!
We know that the ratio of toads to frogmen is 7 : 2. We also know there were 98 actual toads. Therefore we can set up our equations!
[tex]ratio_{toads}=ratio_{frogmen}\\actual_{toads}=actual_{frogmen}\\\\7=2\\98 = x\\\\7x=196\\x=28[/tex]
The first two equations above everything is how you would have everything set up! The second equations under them are the numbers plugged in, and the rest is just simplification.
So, your final answer should be 28 frogmen!
What are the origins of matrices?
Answers
Answer: The origins of matrices can be traced back to the 18th century, with the work of mathematicians such as Gabriel Cramer, Leonhard Euler, and Joseph-Louis Lagrange. These mathematicians developed the idea of using arrays of numbers to represent systems of linear equations, which led to the development of the concept of matrices.
The term "matrix" itself was first used by James Joseph Sylvester in 1850, although it had been in use informally for some time before then. In 1858, the English mathematician Arthur Cayley first published a systematic theory of matrices, which further developed the field.
Matrix theory was primarily used in the early days to solve systems of linear equations, but it soon found applications in areas such as linear algebra, multivariate statistics, and even quantum mechanics.
In summary, the origins of matrices can be traced back to the 18th century as an idea to represent systems of linear equations, which developed over time with contributions of many mathematicians over the centuries, and now it plays an important role in many field of mathematics and science.
Step-by-step explanation:
Five more than a number is greater than 26
Answers
x > 21
The number is greater than 21
Now solve for x. 26-5=21
X>21
Find the surface area and volume for this following pyramid
Answers
Answer:
the aswer is A i did this
Step-by-step explanation
The number of views for a video on a social media website doubles every day. You begin observing the
number of views 8 days after the video was introduced. The number y of views x days after the video is introduced is
represented by the function = 22(2^x-8). When will there be one million views?
Answers
The total number of times social media browsers have been showed your content.
How is social media value calculated?A general, but simplified earned media value formula is: EMV = impressions x cost per 1000 impressions x adjustable variable. The adjustable variable can be anything you are looking to track like engagement or impressions.
Simplifying
22 = 2(x + 8)
Reorder the terms:
22 = 2(8 + x)
22 = (8 * 2 + x * 2)
22 = (16 + 2x)
Solving
22 = 16 + 2x
Solving for variable ‘x’.
Move all terms containing x to the left, all other terms to the right.
Add ‘-2x’ to each side of the equation.
22 + -2x = 16 + 2x + -2x
Combine like terms: 2x + -2x = 0
22 + -2x = 16 + 0
22 + -2x = 16
Add ‘-22’ to each side of the equation.
22 + -22 + -2x = 16 + -22
Combine like terms: 22 + -22 = 0
0 + -2x = 16 + -22
-2x = 16 + -22
Combine like terms: 16 + -22 = -6
-2x = -6
Divide each side by ‘-2’.
X = 3
Simplifying
X = 3
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Part A
GEOMETRY Consider a trapezoid that has one base that measures five feet greater than its height. The other base is one foot less than twice its height. Let x represent the height.
a. Write an expression for the area of the trapezoid.
A=(blank)x^2 +(blank)x ft^2
PART B Write an expression for the area of the trapezoid if its height is increased by 4 feet
A=(blank)x^2+(blank)x+(blank)ft^2
Answers
The area of the trapezoid is 1.5x² + 2x. If the height is increased by 4 feet, the new area would be 1.5x² + 8x
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
Let x represent the height of the trapezoid.
a) One base of trapezoid measures five feet greater than its height. Hence:
First base = x + 5
The other base is one foot less than twice its height, hence:
Second base = 2x - 1
Area = (1/2)(sum of bases) * height = (1/2)(x + 5 + 2x - 1)(x) = 1.5x² + 2x
b) The height is increased by 4 feet. New height = x + 4
First base = (x + 4) + 5 = x + 9
Second base = 2(x + 4) - 1 = 2x + 7
Area = (1/2)(sum of bases) * height = (1/2)(x + 9 + 2x + 7)(x) = 1.5x² + 8x
The area of the trapezoid is 1.5x² + 2x.
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I REALLY NEED HELP WITH PLINK A PLUNK
Answers
Therefore ,We can see that in equation 1 plunk yields the most lorgs at 30. So the plunk coin is the most valuable.
Describe equation.A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 5x - 5 = 25 is an equation. We can find that the variable x has a value of 6 by resolving this equation.
Here,
we need to convert everything to the same unit in order to establish a legitimate comparison when comparing units like inches, feet, and yards. Therefore, we would have to convert everything, for example, to inches. For these five coins, the same concept holds true. Either lorgs, sinds, plunks, harps, or dalts must be used for everything (pick one of those five).
It's equivalent to attempting to change a dollar amount into cents (for example, $1.37 becomes 137 cents). The alternative is to think about it as 1 dollar = 100 cents, 1 quarter = 25 cents, 1 dime = 10 cents, and so on.
The procedures in the various parts below are designed to convert all coinage to lorgs, which will serve as our base unit. Trial and error led me to the conclusion that the lorg coin had the lowest worth, thus I'm striving to obtain everything in lorgs.
The four equations provided are
4 lorgs to a sind
5 dalts x 2 plunks
2 harps from 5 sinds.
3 harps equal 1 plunk.
In that order, I'll refer to them as equations (1) through (4).
One sind equals four logs (1)
5 sinds = 20 lorgs; add 5 to both sides.
2 harps = 20 lorgs; in the equation, swap out "5 sinds" with "2 harps" (3)
1 harp = 10 lorgs; multiply both sides by 2, then write this as an equation (5)
Equation: 1 plunk = 30 lorgs (6)
Each of those equations enables us to determine the lorg value of the coins sind, dalt, harp, and plunk.
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The complete question is : " A nation has five types of coins: sinds, dalts, lorgs, harps, and plunks.1 sind = 4 lorgs ,2 plunks = 5 dalts ,5 sinds = 2 harps , 1 plunk = 3 harps Which coin is the most valuable? a) sindb) daltc) harpd) plunk"
The market research department of a Company recommends that the Company to manufacture and market a new transistor radio after suitable test. The marketing department also presents the following demand equation.X=5,000-500P i.e. P=10-X/500
Furthermore, the financial department provides the following cost equation: C(X) = 7, 000 + 2x
Using derivatives Find Marginal cost, Marginal revenue and Marginal profit of the company.
Answers
The market research department of a Company recommends that the Company to manufacture and market a new transistor radio after suitable test. The marginal cost of the company is 7000 - 2X and marginal revenue is 10X - X/250.
What is Marginal Cost?Marginal cost is an extra cost per unit incurred when an extra unit of output produced or service rendered. Or in other words it can be said that marginal cost is an element of additional unit cost that incurred due to production of goods or services. Some time it is also considering as relevant cost or variable cost.
So in order to compute the transistor manufacturing company's marginal cost, marginal revenue and marginal profit of the company one shall equated the derivative function between them.
In micro economics technical relationship between the said marginal terms is written through derivative function:
Revenue = Price × Quantity Demanded,
Profit Maximize Point where Marginal cost is equal to marginal revenue;
MR = MC,
The marketing department also presents the following demand equation:
X = 5,000 - 500 P
P = 10 - (X ÷ 500), where P is Price and X is quantity demand.
Furthermore, the financial department provides the following cost equation:
C(X) = 7, 000 + 2x
So the revenue function by the help of substitution method:
X = 5,000 - 500 P
Revenue = Price × Quantity Demanded,
Revenue = 10 - (X ÷ 500) × X
= 10X - X^2 ÷ 500
Marginal Revenue! = 10X - !2X/500 = 10X - X/250
Marginal Cost = 7, 000 + 2 (5,000 - 500 P)
= 7000 + 10000 - 1000 P
= 17000 - 1000 ( 10 - (X ÷ 500))
= 17000 - 10000 - 2X
= 7000 - 2X
Therefore marginal revenue is revenue or additional earning made by a seller by selling an extra unit. Revenue is earned when extra unit is being sold.
Learn more about marginal cost:
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